REU Site: Undergraduate Research in Applied Analysis at West Virginia University

这个项目是由数学科学部的劳动力计划和建立的激励竞争性研究计划(EPSCoR)共同资助的。本科生研究体验(REU)SITE奖将支持西弗吉尼亚大学在2024年、2025年和2026年夏季对10名学生进行为期8周的数学培训。该计划将使参与者参与应用分析和偏微分方程式研究。在从全国范围内招聘的同时，将特别考虑代表性不足的群体、在阿巴拉契亚地区及其他地区的学院和大学参加学士学位课程的学生，以及总体上研究机会有限的机构。通过每周的互动、培训和指导，参与者将完成一个独立的研究项目，获得对数学研究的严酷和最佳实践的第一手经验，并熟悉对研究生院和从事数学职业的主流期望。该计划还将有助于加强STEM教育，并将人才吸引到西弗吉尼亚州，从而增强该地区的劳动力和发展。参与者的研究项目将侧重于利用分析和偏微分方程的工具来解决物理和材料科学中出现的实际问题。这些项目包括基于教师导师的研究兴趣的各种主题的集合：具有奇异解的守恒定律和平衡律系统，基本宇宙学模型的渐近性，以及具有电磁波的指向场模型。双曲型守恒律的研究将集中于求解具有特殊初始条件的方程，并采用特征线法和具有几何色彩的各种动力系统思想。这些方法将帮助我们在流体力学、生物科学和宇宙学等许多应用中获得对更一般问题的定量和定性见解。通过对指向场模型的分析，可以加深我们对液晶中弹性波与电磁波相互作用的理解。对粘性粒子模型的研究将增强我们对宇宙中通过物质吸积形成大尺度结构的理解；更具体地说，该项目的这一部分将涉及离散粒子演化方法，以洞察恒星和银河系星系团的长期行为。这个REU的建议项目是基于有趣的开放问题，并被设计成对有才华的本科生来说是容易理解的，同时也是高度智力刺激的。更多信息将在网页上提供：https://mathanddata.wvu.edu/students/undergraduate/applied-analysis-reu.This奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project is jointly funded by the Workforce program in the Division of Mathematical Sciences and the Established Program to Stimulate Competitive Research (EPSCoR). This Research Experiences for Undergraduates (REU) site award will support the mathematical training of ten students per year at West Virginia University in Morgantown, WV, for eight weeks during the summers of 2024, 2025, and 2026. The program will engage participants in applied analysis and partial differential equations research. While recruiting from a nationwide pool, special consideration will be given to underrepresented groups, students attending baccalaureate degree programs at colleges and universities in the Appalachian region and beyond, and, in general, institutions with limited research opportunities. Through weekly interactions, training, and mentoring, participants are expected to complete an independent research project, obtain first-hand experience with the rigors of and best practices in mathematical research, and familiarize themselves with mainstream expectations for graduate school and pursuing a career in mathematics. This program will also help strengthen STEM education and attract talent to West Virginia, thereby enhancing the region’s workforce and development. Participants' research projects will focus on utilizing tools from analysis and PDEs to address practical issues arising from physics and materials science. The projects include a diverse collection of topics based on the research interests of the faculty mentors: systems of conservation and balance laws with singular solutions, asymptotics for a basic cosmological model, and the director field model with electromagnetic waves. Research in hyperbolic conservation laws will focus on solving equations with special initial conditions and employ the characteristic method and, in general, various dynamical systems ideas with geometric flavor. These methods will help us gain quantitative and qualitative insights into more general problems with many applications, such as fluid mechanics, biosciences, and cosmology. The analysis of the director field model will advance our understanding of the interaction between elastic and electromagnetic waves in liquid crystals. Research on the sticky particles model will enhance our comprehension of the formation of large-scale structures in the universe by accretion of matter; more specifically, this part of the project will involve a discrete particle evolution approach to gain insight into the long-time behavior of stellar and galactic clusters. The proposed projects for this REU are based on interesting open problems and are designed to be accessible, while highly intellectually stimulating, for talented undergraduates. Additional information will be provided on the webpage: https://mathanddata.wvu.edu/students/undergraduate/applied-analysis-reu.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.